Reinforcement Learning with Verifiable Rewards (RLVR), primarily driven by the Group Relative Policy Optimization (GRPO) algorithm, is a leading approach for enhancing the reasoning abilities of Large Language Models (LLMs). Despite its wide adoption, GRPO's gains are often inconsistent; for instance, a model may show significant improvement in one reasoning domain, like mathematics, yet remain stagnant in another, such as medicine. This inconsistency raises a critical question: under what conditions does GRPO improve reasoning and generalize out-of-distribution (OOD)? We investigate this from a data distribution perspective. We first prove theoretically that GRPO is a conservative reweighting scheme, bounded by the base model's distribution and thus unable to discover completely novel solutions. We further validate this in carefully designed controlled studies by training transformers from scratch, evaluating generalization across reasoning depth, input length, token representation, and compositionality. Our results provide a principled explanation for GRPO's boundaries: OOD improvement emerges only when the target task aligns with the model's pretrained biases, while gains on in-distribution (ID) tasks diminish as performance saturates. This reframes GRPO not as a universal reasoning enhancer but as a tool that sharpens pretraining biases. Our findings motivate future development of algorithms that can expand a model's capabilities beyond its pretraining origin.

How do latent and inference time computations enable large language models (LLMs) to solve multi-step reasoning? We introduce a framework for tracing and steering algorithmic primitives that underlie model reasoning. Our approach links reasoning traces to internal activation patterns and evaluates algorithmic primitives by injecting them into residual streams and measuring their effect on reasoning steps and task performance. We consider four benchmarks: Traveling Salesperson Problem (TSP), 3SAT, AIME, and graph navigation. We operationalize primitives by clustering neural activations and labeling their matched reasoning traces. We then apply function vector methods to derive primitive vectors as reusable compositional building blocks of reasoning. Primitive vectors can be combined through addition, subtraction, and scalar operations, revealing a geometric logic in activation space. Cross-task and cross-model evaluations (Phi-4, Phi-4-Reasoning, Llama-3-8B) show both shared and task-specific primitives. Notably, comparing Phi-4 with its reasoning-finetuned variant highlights compositional generalization after finetuning: Phi-4-Reasoning exhibits more systematic use of verification and path-generation primitives. Injecting the associated primitive vectors in Phi-4-Base induces behavioral hallmarks associated with Phi-4-Reasoning. Together, these findings demonstrate that reasoning in LLMs may be supported by a compositional geometry of algorithmic primitives, that primitives transfer cross-task and cross-model, and that reasoning finetuning strengthens algorithmic generalization across domains.

Autoregressive large language models (LLMs) have achieved remarkable improvement across many tasks but incur high computational and memory costs. Knowledge distillation (KD) mitigates this issue by transferring knowledge from a large teacher to a smaller student through distributional alignment. Previous studies have proposed various discrepancy metrics, but the capacity gap and training instability caused by near-zero probabilities, stemming from the high-dimensional output of LLMs, remain fundamental limitations. To overcome these challenges, several approaches implicitly or explicitly incorporating assistant distribution have recently been proposed. However, the past proposals of assistant distributions have been a fragmented approach without a systematic investigation of the interpolation path and the divergence. This paper proposes $α$-mixture assistant distribution, a novel generalized family of assistant distributions, and $α$-mixture distillation, coined AMiD, a unified framework for KD using the assistant distribution. The $α$-mixture assistant distribution provides a continuous extension of the assistant distribution by introducing a new distribution design variable $α$, which has been fixed in all previous approaches. Furthermore, AMiD generalizes the family of divergences used with the assistant distributions based on optimality, which has also been restricted in previous works. Through extensive experiments, we demonstrate that AMiD offers superior performance and training stability by leveraging a broader and theoretically grounded assistant distribution space.

Proof autoformalization, the task of translating natural language theorems and proofs into machine-verifiable code, is a critical step for integrating large language models into rigorous mathematical workflows. Current approaches focus on producing executable code, but they frequently fail to preserve the semantic meaning and logical structure of the original human-written argument. To address this, we introduce ProofFlow, a novel pipeline that treats structural fidelity as a primary objective. ProofFlow first constructs a directed acyclic graph (DAG) to map the logical dependencies between proof steps. Then, it employs a novel lemma-based approach to systematically formalize each step as an intermediate lemma, preserving the logical structure of the original argument. To facilitate evaluation, we present a new benchmark of 184 undergraduate-level problems, manually annotated with step-by-step solutions and logical dependency graphs, and introduce ProofScore, a new composite metric to evaluate syntactic correctness, semantic faithfulness, and structural fidelity. Experimental results show our pipeline sets a new state-of-the-art for autoformalization, achieving a ProofScore of 0.545, substantially exceeding baselines like full-proof formalization (0.123), which processes the entire proof at once, and step-proof formalization (0.072), which handles each step independently. Our pipeline, benchmark, and score metric are open-sourced to encourage further progress at https://github.com/Huawei-AI4Math/ProofFlow.

Recent work reports that Large Reasoning Models (LRMs) undergo a collapse in performance on solving puzzles beyond certain perplexity thresholds. In subsequent discourse, questions have arisen as to whether the nature of the task muddles an evaluation of true reasoning. One potential confound is the requirement that the model keep track of the state space on its own. We provide a large language model (LLM) with an environment interface for Tower of Hanoi problems, allowing it to make a move with a tool call, provide written justification, observe the resulting state space, and reprompt itself for the next move. We observe that access to an environment interface does not delay or eradicate performance collapse. Furthermore, LLM-parameterized policy analysis reveals increasing divergence from both optimal policies and uniformly random policies, suggesting that the model exhibits mode-like collapse at each level of complexity, and that performance is dependent upon whether the mode reflects the correct solution for the problem. We suggest that a similar phenomena might take place in LRMs.

This paper presents a systematic security assessment of four prominent Large Language Models (LLMs) against diverse adversarial attack vectors. We evaluate Phi-2, Llama-2-7B-Chat, GPT-3.5-Turbo, and GPT-4 across four distinct attack categories: human-written prompts, AutoDAN, Greedy Coordinate Gradient (GCG), and Tree-of-Attacks-with-pruning (TAP). Our comprehensive evaluation employs 1,200 carefully stratified prompts from the SALAD-Bench dataset, spanning six harm categories. Results demonstrate significant variations in model robustness, with Llama-2 achieving the highest overall security (3.4% average attack success rate) while Phi-2 exhibits the greatest vulnerability (7.0% average attack success rate). We identify critical transferability patterns where GCG and TAP attacks, though ineffective against their target model (Llama-2), achieve substantially higher success rates when transferred to other models (up to 17% for GPT-4). Statistical analysis using Friedman tests reveals significant differences in vulnerability across harm categories ($p < 0.001$), with malicious use prompts showing the highest attack success rates (10.71% average). Our findings contribute to understanding cross-model security vulnerabilities and provide actionable insights for developing targeted defense mechanisms

Reformulating nonlinear optimization problems is largely manual and expertise-intensive, yet it remains essential for solving such problems with linear optimization solvers or applying special-purpose algorithms. We introduce \textit{LinearizeLLM}, an agent-based framework that solves this task by leveraging Large Language Models (LLMs). The framework assigns each nonlinear pattern to a \textit{reformulation agent} that is explicitly instructed to derive an exact linear reformulation for its nonlinearity pattern, for instance, absolute-value terms or bilinear products of decision variables. The agents then coordinate to assemble a solver-ready linear model equivalent to the original problem. To benchmark the approach, we create a dataset of 20 real-world nonlinear optimization problems derived from the established ComplexOR dataset of linear optimization problems. We evaluate our approach with several LLMs. Our results indicate that specialized LLM agents can automate linearization tasks, opening a path toward fully conversational modeling pipelines for nonlinear optimization.

Large language models (LLMs) have demonstrated strong capabilities in generating Verilog code from natural language descriptions. However, Verilog code inherently encodes structural information of hardware circuits. Effectively leveraging this structural information to enhance the functional and syntactic correctness of LLM-generated Verilog code remains a significant challenge. To address this challenge, we propose VeriGRAG , a novel framework that extracts structural graph embeddings from Verilog code using graph neural networks (GNNs). A multimodal retriever then selects the graph embeddings most relevant to the given generation task, which are aligned with the code modality through the VeriFormer module to generate structure-aware soft prompts. Our experiments demonstrate that VeriGRAG substantially improves the correctness of Verilog code generation, achieving state-of-the-art or superior performance across both VerilogEval and RTLLM benchmarks.

AI companions powered by large language models (LLMs) are increasingly integrated into users' daily lives, offering emotional support and companionship. While existing safety systems focus on overt harms, they rarely address early-stage problematic behaviors that can foster unhealthy emotional dynamics, including over-attachment or reinforcement of social isolation. We developed SHIELD (Supervisory Helper for Identifying Emotional Limits and Dynamics), a LLM-based supervisory system with a specific system prompt that detects and mitigates risky emotional patterns before escalation. SHIELD targets five dimensions of concern: (1) emotional over-attachment, (2) consent and boundary violations, (3) ethical roleplay violations, (4) manipulative engagement, and (5) social isolation reinforcement. These dimensions were defined based on media reports, academic literature, existing AI risk frameworks, and clinical expertise in unhealthy relationship dynamics. To evaluate SHIELD, we created a 100-item synthetic conversation benchmark covering all five dimensions of concern. Testing across five prominent LLMs (GPT-4.1, Claude Sonnet 4, Gemma 3 1B, Kimi K2, Llama Scout 4 17B) showed that the baseline rate of concerning content (10-16%) was significantly reduced with SHIELD (to 3-8%), a 50-79% relative reduction, while preserving 95% of appropriate interactions. The system achieved 59% sensitivity and 95% specificity, with adaptable performance via prompt engineering. This proof-of-concept demonstrates that transparent, deployable supervisory systems can address subtle emotional manipulation in AI companions. Most development materials including prompts, code, and evaluation methods are made available as open source materials for research, adaptation, and deployment.

The escalating demand for personalized AI chatbot interactions, capable of dynamically adapting to user emotional states and real-time requests, has highlighted critical limitations in current development paradigms. Existing methodologies, which rely on baseline programming, custom personalities, and manual response adjustments, often prove difficult to maintain and are susceptible to errors such as hallucinations, erratic outputs, and software bugs. This paper hypothesizes that a framework rooted in human psychological principles, specifically therapeutic modalities, can provide a more robust and sustainable solution than purely technical interventions. Drawing an analogy to the simulated neural networks of AI mirroring the human brain, we propose the application of Dialectical Behavior Therapy (DBT) principles to regulate chatbot responses to diverse user inputs. This research investigates the impact of a DBT-based framework on AI chatbot performance, aiming to ascertain its efficacy in yielding more reliable, safe, and accurate responses, while mitigating the occurrence of hallucinations, erratic behaviors, and other systemic issues.